For a particular data set, the summary statistics are: n = 20 , ∑ f x = 563 , ∑ f x 2 = 16143 . Find the values of the mean and the standard deviation.

Given that, ∑ f x = 563 and ∑ f x 2 = 16143 , n = 20 We know that, mean = ∑ f x n = 563 20 = 28 . 15 Standard deviation, σ = ∑ f x 2 n - ∑ f x n 2 = 16143 20 - 28 . 15 2 = 807 . 15 - 792 . 4225 = 14 . 7275 ≈ 3 . 84

For a particular data set, the summary statistics are: n = 20 , ∑ f x = 563 , ∑ f x 2 = 16143 . Find the values of the mean and the standard deviation.

Given that, ∑ f x = 563 and ∑ f x 2 = 16143 , n = 20 We know that, mean = ∑ f x n = 563 20 = 28 . 15 Standard deviation, σ = ∑ f x 2 n - ∑ f x n 2 = 16143 20 - 28 . 15 2 = 807 . 15 - 792 . 4225 = 14 . 7275 ≈ 3 . 84

Samples of water were taken from a river near a chemical plant to see if there were raised levels of lead. Ten samples were collected, shown in the table below. The units are μ g per liter. 6 . 3 9 . 6 12 . 2 12 . 3 10 . 3 12 . 1 10 . 3 8 . 4 9 . 2 4 . 3 Over 10 μ g per liter of lead in water is dangerous. Comment on whether the lead levels should be investigated furher.

The given data table is 6 . 3 9 . 6 12 . 2 12 . 3 10 . 3 12 . 1 10 . 3 8 . 4 9 . 2 4 . 3 The formula to calculate the mean is μ = ∑ x n . Now, μ = 6 . 3 + 9 . 6 + 12 . 2 + 12 . 3 + 10 . 3 + 12 . 1 + 10 . 3 + 8 . 4 + 9 . 2 + 4 . 3 10 = 95 10 = 9 . 5 μ g The formula to calculate the standard deviation is σ = ∑ x - μ 2 n . Now, Mass g x - μ x - μ 2 6 . 3 - 3 . 2 10 . 24 9 . 6 0 . 1 0 . 01 12 . 2 2 . 7 7 . 29 12 . 3 2 . 8 7 . 84 10 . 3 0 . 8 0 . 64 12 . 1 2 . 6 6 . 76 10 . 3 0 . 8 0 . 64 8 . 4 - 1 . 1 1 . 21 9 . 2 - 0 . 3 0 . 09 4 . 3 - 5 . 2 27 . 04 ∑ x - μ 2 = 61 . 76 Standard deviation = σ = ∑ x - μ 2 n = 61 . 76 10 = 6 . 176 = 2 . 485 μ g Here, the mean as 9 . 5 μ g and the standard deviation as 2 . 485 μ g . Since, the average level of lead in water is 9 . 5 μ g which is less than 10 μ g , so further investigation is not required.

Birth mass follows a normal distribution. The summary statistics for the masses of 50 babies in a hospital were ∑ x = 160 kg and ∑ x 2 = 524 . Calculate the mean baby mass and the standard deviation of the sample.

Given, n = 50 , ∑ x = 160 and ∑ x 2 = 524 We know that, Mean = μ = ∑ x n Now, μ = 160 50 = 3 . 2 We know that σ = ∑ x 2 n - ∑ x n 2 Now, σ = 524 50 - 160 50 2 = 10 . 48 - 3 . 2 2 = 10 . 48 - 10 . 24 = 0 . 24 = 0 . 489 Hence, the mean is 3 . 2 and the standard deviation is 0 . 489 .

MEDIUM

MYP:4-5

IMPORTANT

Earn 100

For a particular data set, the summary statistics are: $n = 20, \sum_{} f x = 563, \sum_{} f x^{2} = 16143$ . Find the values of the mean and the standard deviation.

Important Questions on Standard Deviation

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Mixed practice>Q 6

In a biscuits factory, a sample of 10 packets of biscuits were weighed.

Mass (g)

196

197

199

200

200

200

202

203

203

205

Calculate the mean and standard deviation.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Mixed practice>Q 6

In a biscuits factory, a sample of 10 packets of biscuits were weighed.

Mass (g)

196

197

199

200

200

200

202

203

203

205

To make predictions about the mean and standard deviations of all the packets of biscuits in the factory, which values of the mean and standard deviation would you use?

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Mixed practice>Q 7

Samples of water were taken from a river near a chemical plant to see if there were raised levels of lead. Ten samples were collected, shown in the table below. The units are $μ g$ per liter.

$6.3$	$9.6$	$12.2$	$12.3$	$10.3$
$12.1$	$10.3$	$8.4$	$9.2$	$4.3$

Use this data to predict the mean and standard deviation for the amount of lead in the river.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Mixed practice>Q 7

Samples of water were taken from a river near a chemical plant to see if there were raised levels of lead. Ten samples were collected, shown in the table below. The units are $μ g$ per liter.

$6.3$	$9.6$	$12.2$	$12.3$	$10.3$
$12.1$	$10.3$	$8.4$	$9.2$	$4.3$

Over $10 μ g$ per liter of lead in water is dangerous. Comment on whether the lead levels should be investigated furher.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Review in context>Q 1

Dr Roussianos asked cardiology patients to measure their systolic blood pressure each Saturday morning for ten weeks.

Here is the data for three patients.

Patient $1$

$95$	$95$	$87$	$92$	$100$
$84$	$87$	$90$	$87$	$96$

Patient $2$

$78$	$76$	$75$	$80$	$76$
$75$	$81$	$80$	$82$	$80$

Patient $3$

$65$	$100$	$76$	$98$	$58$
$75$	$76$	$98$	$66$	$75$

This table shows the treatments recommended for different values of the yearly mean and standard deviation.

Mean	Standard deviation	Treatment
$< 75$	$< 10$	low blood pressure treatment
$75 - 85$	$< 10$	no treatment
$> 85$	$< 10$	high blood pressure treatment
any value	$> 10$	more tests needed

Calculate the mean and use the sample data to estimate the yearly statistics and therefore help to determine the treatment for each patient.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Review in context>Q 2

$80$ people were asked to measure their pulse rate as soon as they woke up in the morning.

The summary statistics are: $\sum_{} x = 6000$ and $\sum_{} x^{2} = 452450$ .

From this information, find the mean and the standard deviation of the data set. If this was a sample of the population, state the inferences which could be drawn from this sample data set.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Review in context>Q 3

Birth mass follows a normal distribution. The summary statistics for the masses of $50$ babies in a hospital were $\sum_{} x = 160 kg$ and $\sum_{} x^{2} = 524$ .

Calculate the mean baby mass and the standard deviation of the sample.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 7 - Standard Deviation>Review in context>Q 3

Birth mass follows a normal distribution. The summary statistics for the masses of $50$ babies in a hospital were $\sum_{} x = 160 kg$ and $\sum_{} x^{2} = 524$ .

If a baby's mass is less than $2.5$ times the standard deviation below the mean, the baby is at risk. Find a value of $x$ , so that babies who weigh less than $x$ kg are considered to be at risk.

For a particular data set, the summary statistics are: n=20, ∑fx=563, ∑fx2=16143. Find the values of the mean and the standard deviation.

Important Questions on Standard Deviation

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For a particular data set, the summary statistics are: $n = 20, \sum_{} f x = 563, \sum_{} f x^{2} = 16143$ . Find the values of the mean and the standard deviation.